1. Standard error for the following data
10,20,30,40, Significance Level `alpha=0.05` and One-tailed test
Solution:
`bar x=25` and Variance `sigma^2=166.6667` for `10,20,30,40`
| `x` | `x - bar x = x - 25` | `(x - bar x)^2` |
| 10 | -15 | 225 |
| 20 | -5 | 25 |
| 30 | 5 | 25 |
| 40 | 15 | 225 |
| --- | --- | --- |
| `sum x=100` | `sum (x - bar x)=0` | `sum (x - bar x)^2=500` |
Mean `bar x = (sum x)/n`
`=(10 + 20 + 30 + 40)/4`
`=100/4`
`=25`
Sample Variance `S^2 = (sum (x - bar x)^2)/(n-1)`
`=500/3`
`=166.6667`
`sigma=sqrt(sigma^2)=sqrt(166.6667)=12.9099`
Standard Error `=(sigma)/sqrt(n)=12.9099/sqrt(4)=12.9099/2=6.455`
This material is intended as a summary. Use your textbook for detail explanation.
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